Shape memory alloys (SMAs) are materials that exhibit a distinct thermomechanical coupling, one that gives rise to a wide variety of applications across a broad range of fields. One of the most successful roles is in the construction of novel medical implants. Unfortunately, concerns have been raised about the biocompatibility of the most popular SMA, nitinol (NiTi), due to the known toxic, allergenic and carcinogenic properties of nickel. Given the unique capabilities of SMAs, it is apparent that there is a need for a new class of alloys - alloys that exhibit the full range of shape memory abilities yet are also free of any undesirable side effects. This article reviews the literature surrounding SMAs and identifies the metals Ti, Au, Sn, Ta, Nb, Ru and Zr as candidates for the production of thoroughly biocompatible SMAs. Hf and Re are also promising, though more research is necessary before a definitive statement can be made. Further, the Ti-(Ta,Nb)-(Zr,Hf) alloy system is particularly suited for orthopaedic implants due to a reduced Young's modulus. However, concerns over this system's shape memory properties exist, and should be taken into consideration. Alternate alloy systems that demonstrate higher bulk moduli may still be considered, however, if they are formed into a porous structure. Due to the nature of the alloying components, blended elemental powder metallurgy is recommended for the manufacture of these alloys, particularly due to the ease with which it may be adapted to the formation of porous alloys.